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Mathematics
Problem
The line
2
x
+
y
=
1
2x + y = 1
2
x
+
y
=
1
is tangent to the hyperbola
x
2
a
2
−
y
2
b
2
=
1
\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
a
2
x
2
−
b
2
y
2
=
1
. If this line passes through the point of intersection of the nearest directrix and the X-axis, then the eccentricity of the hyperbola is
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